Stability in a job market with linearly increasing valuations and quota system

We consider a job market in which preferences of players are represented by linearly increasing valuations. The set of players is divided into two disjoint subsets: a set of workers and a set of firms. The set of workers is further divided into subsets, which represent different categories or classes in everyday life. We consider that firms have vacant posts for all such categories. Each worker wants a job for a category to which he/she belongs. Firms have freedom to hire more than one worker from any category. A worker can work in only one category for at most one firm. We prove the existence of a stable outcome for such a market. The college admission problem by Gale and Shapley is a special case of our model.